Article pubs.acs.org/est
Vapor−Wall Deposition in Chambers: Theoretical Considerations Renee C. McVay,† Christopher D. Cappa,‡ and John H. Seinfeld*,†,§ †
Division of Chemistry and Chemical Engineering and §Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, United States ‡ Department of Civil and Environmental Engineering, University of California at Davis, Davis, California 95616, United States S Supporting Information *
ABSTRACT: In order to constrain the effects of vapor−wall deposition on measured secondary organic aerosol (SOA) yields in laboratory chambers, researchers recently varied the seed aerosol surface area in toluene oxidation and observed a clear increase in the SOA yield with increasing seed surface area (Zhang, X.; et al. Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 5802). Using a coupled vapor− particle dynamics model, we examine the extent to which this increase is the result of vapor−wall deposition versus kinetic limitations arising from imperfect accommodation of organic species into the particle phase. We show that a seed surface area dependence of the SOA yield is present only when condensation of vapors onto particles is kinetically limited. The existence of kinetic limitation can be predicted by comparing the characteristic time scales of gas-phase reaction, vapor− wall deposition, and gas−particle equilibration. The gas−particle equilibration time scale depends on the gas−particle accommodation coefficient αp. Regardless of the extent of kinetic limitation, vapor−wall deposition depresses the SOA yield from that in its absence since vapor molecules that might otherwise condense on particles deposit on the walls. To accurately extrapolate chamber-derived yields to atmospheric conditions, both vapor−wall deposition and kinetic limitations must be taken into account.
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INTRODUCTION The formation of secondary organic aerosol (SOA) is represented in atmospheric models by SOA yields (mass of SOA formed per mass of parent volatile organic compound (VOC) reacted), which are determined in laboratory chambers. It has been established that current atmospheric models using chamber-derived yields significantly underpredict ambient SOA levels.1−7 Recent work has suggested that experimentally determined SOA yields could be systematically biased low due to wall deposition of organic vapors that would otherwise contribute to SOA growth.8−10 Zhang et al.11 reported the results of chamber studies aimed to constrain experimentally the effect of vapor−wall deposition on SOA yields. In these experiments, involving toluene as the parent VOC, the level of seed aerosol was systematically varied in order to modulate the competition between growing particles and the chamber walls for condensable vapors. The statistical oxidation model of Cappa et al.,12,13 updated to account for dynamic partitioning between vapors and particles and vapors and the chamber walls, was fit to the data. The results demonstrate clear experimental evidence of the role of vapor−wall deposition on measured SOA yield. The present work analyzes theoretically the observed dependence of SOA yields on seed surface area by simulating the key elements of VOC oxidation and aerosol chamber dynamics. The representation of gas-phase VOC oxidation chemistry in such an analysis need not be complex, as the essential factors are the rate of progressive oxidation and the volatilities of the oxidation products. The present study is intended to provide a theoretical © 2014 American Chemical Society
structure for assessing the effects of key processes on vapor− wall deposition in laboratory chamber studies of SOA formation.
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METHODS
Gas-Phase VOC Oxidation. To evaluate theoretically the effect of vapor−wall deposition in a typical chamber experiment, the gas-phase chemistry need only represent the progressive oxidation of a parent VOC. We consider oxidation of a parent VOC, species A, occurring sequentially according to A→B→C→D. Species A represents the completely volatile parent VOC, and species B−D are oxidation products, with mass saturation concentrations decreasing by 1 order of magnitude per generation of reaction. Each oxidation step can be considered to represent reaction with OH, although the chemical details are not required. With no loss of generality, each species in this idealized mechanism is assigned the same molecular weight (200 g mol−1); in so doing, the maximum SOA yield possible is 1.0. Since oxidation leads to progressively lower volatility species, the maximum yield will always be reached at sufficiently long time if there are no additional vapor loss mechanisms, such as wall deposition. Received: Revised: Accepted: Published: 10251
May 2, August August August
2014 4, 2014 5, 2014 13, 2014
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Ji = 2πDiDp(Gi − Gieq )FFS
Aerosol Dynamic Model. We have developed a coupled vapor−particle dynamics model following the framework of the aerosol parameter estimation (APE) model of Pierce et al.14 The model simulates coagulation, condensation/evaporation, and particle−wall and vapor−wall deposition in a well-mixed laboratory chamber in which a VOC is being oxidized to SOA. The SOA yield is determined as the ratio of the total mass of organic oxidation products condensed on both suspended and wall-deposited particles to the total mass of VOC reacted (both expressed in units of μg m−3). The aerosol size distribution is represented using fixed size bins, with specified mean diameters, so that the evolution of the chamber aerosol is reflected by the time variation of the particle number concentration in each bin. The aerosol general dynamic equation is expressed in terms of the particle size distribution function n(Dp,t) as
where Gi represents the gas-phase concentration of species i, and Geq is the equilibrium gas-phase concentration, both i expressed in μg m−3. Di is the molecular diffusivity of species i in air. The Fuchs−Sutugin correction for non-continuum gasphase diffusion is15 FFS =
parameter
(1)
αp
where Dp is the particle diameter. The equation governing the change in the number distribution due to coagulation is14,15
A/V αwall
⎛ ∂n(Dp , t ) ⎞ ⎜⎜ = ⎟⎟ ∂t ⎝ ⎠coag
∫0
K[(Dp3
− n(Dp , t )
∫0
Ci* Cw 3 1/3
−q)
,
q]n[(Dp3)1/3 ,
t ]n(q , t ) dq
Di G0A
∞
K (q , Dp)n(q , t ) dq
ke k[OH]A→B
(2) 15
where K(Dp1,Dp2) is the coagulation kernel between particles of diameters Dp1 and Dp2. The change in aerosol number distribution due to particle wall deposition is expressed as ⎛ ∂n(Dp , t ) ⎞ ⎜⎜ ⎟⎟ = −β(Dp)n(Dp , t ) ∂t ⎝ ⎠ wall loss
Kn + Kn + 0.283Knαp + 0.75αp
(5)
Table 1. Simulation Parameters
⎛ ∂n(Dp , t ) ⎞ ⎟⎟ + ⎜⎜ ∂t ⎝ ⎠ wall loss
Dp
0.75αp(1 + Kn) 2
where αp is the accommodation coefficient of the vapor species on the particle. Kn is the Knudsen number, defined as Kn = 2λAB/Dp. λAB is the mean free path of the diffusing molecule in air, given by λAB = 3Di/cA̅ , and cA̅ is the mean speed of the diffusing molecule, cA̅ = (8RT/πMA)1/2, where R is the ideal gas constant, T is the temperature, and MA is the molecular weight of the diffusing molecule. Numerical values for all parameters that are used in the simulations are given in Table 1. Equations
⎛ ∂n(Dp , t ) ⎞ ⎛ ∂n(Dp , t ) ⎞ ⎛ ∂n(Dp , t ) ⎞ ⎜⎜ ⎟⎟ = ⎜⎜ ⎟⎟ ⎟⎟ + ⎜⎜ ∂t ∂t ∂t ⎝ ⎠ ⎝ ⎠coag ⎝ ⎠cond/evap
1 2
(4)
kwall,on Mi Minit P ρ T
(3)
where β(Dp) is the size-dependent first-order loss rate coefficient. The β(Dp) values used in the present simulations are those determined experimentally for the Caltech chamber.16 Particles that deposit on the wall during the course of an experiment are treated theoretically in one of two ways for computing the SOA yield.16 In the so-called lower limit, once particles are lost to the walls, they are assumed to cease participation in condensation/evaporation or coagulation. The mass of condensed oxidation products on each particle at the time of its deposition is added to that of suspended particles in computing the SOA yield. The lower limit will be used in the simulations presented here. Historically, yields have also been reported using the so-called upper limit, in which particles lost to the wall are assumed to continue to participate in condensation/evaporation as if they had remained suspended. This approach includes some transfer of organic vapors to chamber walls but does not account for differences in wall versus particle transport time scales.11 The rate of vapor condensation onto a spherical aerosol particle can be expressed as15
definition accommodation coefficient of vapor species on particle surface-area-to-volume ratio of the chamber accommodation coefficient of vapor species on the wall saturation concentrations for species B−D equivalent wall organic aerosol concentration gas-phase diffusivity of species i initial parent VOC concentration coefficient of eddy diffusion in chamber product of reaction rate constant and OH concentration first-order vapor−wall deposition coefficient species molecular weight initially absorbing organic material in seed aerosol pressure particle density temperature
value varied 1.6 m−1 10−5 [101 100 10−1] μg m−3 10 mg m−3 3 × 10−6 m2 s−1 327 μg m−3 (40 ppb) 0.015 s−1 10−5 s−1 1.7 × 10−4 s−1 200 g mol−1 0.01 μg m−3 1 × 105 Pa 1700 kg m−3 298 K
4 and 5 are applied in each size bin to calculate the condensation or evaporation flux of each vapor species to or from a single particle and then scaled by the number concentration of particles in that size bin. The flux summed over all size bins produces the rate of change of each vapor species due to evaporation or condensation. The vapor−particle accommodation coefficient αp encompasses all resistances to vapor−particle mass transfer, including surface accommodation and diffusion limitations in the particle phase.17,18 Vapor−particle accommodation coefficients are difficult to predict from molecular properties alone, but have been measured experimentally in both thermodenuders and evaporation chamber studies.17−21 A range of values have been determined, even for the same systems. For example, Stanier et al.19 measured evaporation rates of α-pinene SOA using tandem differential mobility analysis and found accommodation coefficients 10−5 (see Figure S4 in ref 11). Matsunaga and Ziemann9 showed that vapor species can dissolve and equilibrate in the Teflon walls of conventional laboratory chambers and introduced the parameter Cw to represent the capacity of Teflon to take up organics. While Cw has units of concentration, it does not necessarily represent a physical layer of organic material on the wall. In the present model, vapor interaction with the wall is similarly assumed to be reversible, with a rate of desorption of kwall,off:9
(6)
In this equation, Ai is the concentration of species i in the particle phase, C*i is the saturation concentration of species i, ∑kAk is the sum of all species in the condensed phase, of which i is a subset, and Minit is the mass concentration of any initially present absorbing organic concentration, all expressed in terms of μg m−3 of air. In general, Geq i varies for each size bin, based on the mass concentration of species i and the total organic concentration in that size bin. For computational convenience, owing to the presence of coagulation, the concentration of each organic species i in each size bin is not tracked dynamically; only the total condensed mass of each species over the entire size distribution is determined. The total mass in each size bin is also tracked, but this mass is not resolved into organic and inorganic masses because the number of particles in each size bin changes with time. Consequently, Geq i is calculated globally over the entire size distribution, based on the total mass of condensed species i and the total mass of condensed organics. (The total amount of species i in the condensed phase includes, as noted, the mass condensed onto particles that subsequently deposited on the wall.) We validated that this simplification of the actual size-dependent concentration dynamics captures the basic dependence of SOA yield on aerosol surface area by creating an equivalent moving bin model without coagulation, in which the total number of particles in each bin is conserved. The concentrations of each species i in each bin are then used to calculate Geq i for each bin. SOA yields predicted in this manner are virtually identical to those of the fixed bin model. A nominal (0.01 μg m−3) nonvolatile initial organic seed aerosol concentration, Minit, is assumed to be present in the chamber regardless of initial inorganic seed number concentration merely to avoid numerical errors in eq 6 at the first time step. Results are insensitive to this value up to 1 μg m−3. Simulations (not shown) demonstrate that including the Kelvin effect in the calculation of the equilibrium vapor pressure has a negligible influence on the computed SOA yields for size distributions typical of seeded SOA chamber experiments. Vapor−wall deposition is assumed to occur for species B−D and is characterized by a first-order deposition coefficient, kwall,on:26
k wall,off =
k wall,on K w Cw
⎛ C *M γ ⎞ i w w⎟ = k wall,on⎜⎜ ⎟ C M ⎝ w pγp ⎠
(8)
where Kw is the vapor−wall partitioning coefficient, Mw is the effective molecular weight of the wall material, γw is the activity coefficient of the species in the wall layer, Mp is the average molecular weight of the organic species in the particle, and γp is the activity coefficient of the species in the particle. This equation is derived using the definition Kw = RT/MwγwP°i and the relationship C*i = MpγpP°i /RT to convert vapor pressure P°i into saturation concentration.9 For convenience, we assume that Mw = Mp and γp = γw.11 As noted, the saturation concentration C*i is taken to decrease progressively by 1 order of magnitude for species B−D. The nominal value for Cw is set at 10 mg m−3, based on observations of Matsunaga and Ziemann9 that Cw varies between 2 and 24 mg m−3 for different compounds. Numerical Experiments. The coupled vapor-aerosol dynamics-wall model is used to explore the sensitivity of SOA yield to vapor−wall deposition. The assumed seed aerosol size distribution is based on typical distributions in the Caltech laboratory chamber, encompassing 53 size bins, spanning the diameter range from 15 to 800 nm and log-normal with a standard deviation of 1.5. The initial particle number concentration is varied for different simulations in order to vary the total initial seed surface area. For each combination of parameters, seven different initial particle number concentrations, given in Table 2, are used in order to generate seven initial seed surface areas. The ratio of the initial seed surface area to the surface area of the chamber walls, based on the Caltech laboratory chambers, is also given in Table 2 for each case. The estimated surface area of the Caltech chamber is 41 m2 assuming a rectangular shape with sides of 2.74, 2.43, and 2.69 m. Each simulation is run for 20 h of oxidation, and the SOA yield is calculated at the end of each simulation. 10253
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Table 2. Assumed Initial Aerosol Number Distribution Parameters
case
initial particle concentration (cm−3)
mean particle diameter (nm)
1 2 3 4 5 6 7
10 000 20 000 50 000 100 000 200 000 400 000 600 000
100 100 100 100 100 100 100
initial particle surface area (μm2 cm−3) 4.4 8.7 2.2 4.4 8.7 1.7 2.6
× × × × × × ×
102 102 103 103 103 104 104
ratio of initial particle SA to wall SA 2.7 5.3 1.3 2.7 5.3 1.1 1.6
× × × × × × ×
10−4 10−4 10−3 10−3 10−3 10−2 10−2
The parameters used in each simulation are given in Table 1. For k[OH]A→B, the base value is assigned as 10−5 s−1 to represent the product of the toluene−OH rate constant of 5.6 × 10−12 cm3 molec−1 s−1 and an OH concentration of ∼2 × 106 molec cm−3, the approximate value observed during the toluene SOA experiments in ref 11. The k[OH] for each successive reaction, B → C, etc., is assumed to be five times the previous k[OH] in order to approximate the increase in reaction rate as species become more oxidized. Results are insensitive to this reaction rate scaling factor for values between 1 and 5. αp is varied from 0.001, the best-fit value determined by ref 11, to 1, the ideal accommodation. The saturation concentrations for species B−D are set as [101 100 10−1] μg m−3.
Figure 1. Final organic aerosol concentration COA after 20 h of simulation as a function of the initial seed surface area for simulations beginning with 40 ppb of parent VOC. Conditions for the simulations are given in Tables 1 and 2. Different combinations of αp and presence or absence of wall deposition are shown. The pie charts at the right show the product distribution at the end of the simulation at the highest seed surface area considered for each of the six simulations. The pie charts appear top to bottom in the same top-to-bottom order as the COA curves.
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RESULTS AND DISCUSSION Increased Partitioning versus Wall Deposition Effect. The clear increase in SOA yield observed by Zhang et al.11 with increased seed particle surface area can arise from two separate effects: (1) increased organic aerosol concentration COA via gas−particle partitioning if condensation is kinetically limited, or (2) reduction in the deposition of vapor organics to the wall. To evaluate these separate, but potentially overlapping, effects, numerical experiments were performed with different αp values and in the presence or absence of vapor−wall deposition at varying initial seed surface areas. Figure 1 shows COA at the end of 20 h numerical experiments starting with a parent VOC mixing ratio of 40 ppb (concentration G0A = 327 μg m−3). Pie charts are shown giving the distribution of products in the organic aerosol phase at the end of the simulations for the highest initial seed surface area. For αp = 0.001, COA increases as surface area increases both in the presence and absence of vapor−wall deposition. The surface area dependence of COA even in the absence of vapor−wall deposition indicates that the observation of surface area-dependent yields is not sufficient to prove the existence of vapor−wall deposition. The increase in COA in both the presence and absence of wall deposition is attributable to the kinetic limitations on organic vapor condensation on particles imposed by a low value of αp. This limitation is illustrated by comparing the characteristic time scale for gas−particle equilibration with the time scales for reaction and wall deposition (Figure 2). The characteristic time scale for gas−particle equilibration τg,p (i.e., the e-folding time for an aerosol to reestablish vapor−particle equilibrium after a slight perturbation) is15 1 τg,p = 2πDi(∑bins n(Dp)DpFFS) (9)
Figure 2. Equilibration time scale for gas−particle partitioning as a function of the initial seed surface area for different values of the vapor−particle accommodation coefficient, αp. The equilibration time scale for gas−wall partitioning (τg,w = 1/kwall,on) and the time scale for reaction (τrxn = 1/(k[OH]C→D)) are shown as horizontal lines, as these time scales are independent of seed surface area.
This time scale is not necessarily that for vapor and particle phases to establish equilibrium in an SOA formation experiment, which depends on other factors such as the rate of reaction and the volatilities of the products.27 In Figure 2, τg,p is calculated on the basis of the initial size distribution, but its value will change with time as n(Dp) in each size bin evolves (as discussed below). Quasi-equilibrium growth occurs when the net production rate of condensable vapors is slow compared to the time to establish gas−particle equilibrium; in this limit, the vapor and particle phases maintain equilibrium.28,29 The magnitude of τg,p relative to time scales for other processes in the system governs the transition between kinetically limited and quasi-equilibrium growth.28 Gas−particle equilibrium is governed by the total organic mass in the system and is not 10254
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dependent on the surface area of the inorganic seed. In contrast, kinetically limited condensation, when τg,p is competitive with the time scale for production of condensable vapors, depends on the aerosol surface area. The reaction time scale τrxn controls the production rate of condensable vapors. In Figure 2, τrxn is calculated on the basis of k[OH]C→D because this reaction controls the production rate for the least volatile species. For αp = 0.001, τg,p exceeds τrxn at the lowest seed surface areas, indicating that condensation is kinetically limited, and COA for αp = 0.001 in the absence of wall deposition in Figure 1 consequently increases sharply with seed surface area. As the seed surface area increases at αp = 0.001, τg,p becomes an order of magnitude smaller than τrxn, and COA achieves a plateau at the highest seed surface areas. As αp increases, τg,p decreases with respect to τrxn and condensation shifts toward quasiequilibrium growth. This shift is evident in Figure 1, as COA in the absence of wall deposition becomes less dependent on seed surface area as αp increases. The presence of vapor−wall deposition introduces an additional time scale into the system, τg,w = 1/kwall,on, the characteristic time scale of vapor−wall deposition. τg,p must be less than τrxn and τg,w for quasi-equilibrium growth. When τrxn ≈ τg,w, COA in the presence of vapor−wall deposition becomes less dependent on seed surface area as αp increases. Ehn et al.30 observed SOA yields from the ozonolysis of α-pinene to increase with increasing particle surface area but required αp = 1.0 to fit the observed growth data. The observed vapor−wall deposition rate was much greater in their continuously stirred reactor than that in the Caltech chamber (0.011 s−1 versus 2.5 × 10−4 s−1). In their reactor, τg,p ≈ τg,w even at αp = 1.0, and condensation is kinetically limited. The presence of vapor−wall deposition depresses the SOA yield from that calculated in the absence of wall deposition regardless of the value of αp, as seen in Figure 1. Condensation that is kinetically limited produces a narrowing of the particle size distribution, while condensation dominated by quasi-equilibrium growth produces a broadening of the size distribution.28,29 If condensation shifts toward quasi-equilibrium growth as seed surface area is increased, the evolution of the particle size distribution should theoretically reflect this shift. However, as seed surface area is increased, coagulation will become more important and may mask any broadening of the size distribution, as smaller particles are scavenged by larger particles. Particle distributions shown in the pie charts to the right of Figure 1 demonstrate another effect of changing the gas− particle equilibration time: decreasing τg,p by increasing αp shifts the product distribution toward earlier generation products. As τg,p decreases, partitioning of species B to the particle increases preferentially relative to conversion to C and (in the presence of wall deposition) deposition to the walls. Yields as a function of COA at a constant temperature have historically been parametrized for use in air quality models (AQMs) such as CMAQ31 with models such as the twoproduct model and the volatility basis set (VBS),32 each of which assumes instantaneous gas−particle equilibrium. As shown in Figure 1, for αp = 0.001 in this system, condensation is kinetically limited. Consequently, yields simulated starting with varying G0A and at varying seed surface areas cannot be described by a single two-product or VBS fit (Figure 3). The points in Figure 3 were generated by varying both G0A and seed surface area with (circles) and without (diamonds) vapor−wall deposition. The size of the markers increases as G0A increases,
Figure 3. SOA yields after 20 h of simulation as a function of the final organic aerosol concentration COA for αp = 0.001. The points on the curve were generated by varying the initial parent VOC concentration G0A with (circles) and without (diamonds) vapor−wall deposition. The size of the markers increases as G0A increases and colors correspond to different values of the initial seed surface area. The lines were generated by fitting a two-product model to the data points.
and colors correspond to different values of the initial seed surface area. For simplicity, the lines were generated by fitting a two-product model to the data points. (This fit merely illustrates the discrepancy between the simulation results and common partitioning model predictions.) For a fixed GA0 (indicated in Figure 3 by markers of the same size), the SOA yield increases as both COA and seed surface area increase. At a fixed seed surface area, the yield increases as G0A and COA increase. For a fixed final COA (visualized by drawing vertical lines in Figure 3), the yield increases as seed surface area increases and G0A decreases. As a result of the kinetic limitation imposed by the low αp, the yields depend on G0A in addition to the seed surface area because the time required to reach a fixed COA depends on both parameters. As surface area increases, the same final COA is achieved with decreasing G0A, and the lower ΔVOC results in a higher yield. By contrast, Figure S1 shows simulations with αp = 0.01, i.e., 10 times larger. In the absence of vapor−wall deposition, condensation shifts toward quasi-equilibrium growth with the higher αp, and the yields approach a single curve with little seed area dependence. Yields calculated in the presence of vapor− wall deposition for αp = 0.01 maintain a seed surface area dependence at low seed surface areas but lose this dependence at the highest surface areas. If a similar plot is generated for αp = 1.0 (not shown), yields in the presence and absence of wall deposition collapse onto single (but separate) curves. This further illustrates that yields increase as seed surface area increases only when condensation is kinetically limited. Influence of Volatility Distributions. The simulations are based on saturation concentrations that decrease by an order of magnitude per each generation of reaction. Different combinations of saturations concentrations were also used with αp = 0.001: C*B = 102 μg m−3 with subsequent saturation concentrations decreasing by an order of magnitude per generation, CB* = 102 or 103 μg m−3 with subsequent saturation concentrations decreasing by 2 orders of magnitude per generation, and all saturation concentrations set to zero. Each combination produces similar dependence of yield on seed surface area and a depression of the yield due to vapor−wall 10255
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Evolution of τg,p. The preceding analysis has been based on an assumed initial seed aerosol size distribution: yields are determined as a function of the initial seed surface area, and τg,p (Figure 2) is calculated on the basis of the initial size distribution. The aerosol size distribution changes continuously as particles grow by condensation and are lost by coagulation or wall deposition. To examine the extent to which the initial size distribution is a robust metric for comparing different experimental conditions, we consider the time evolution of τg,p for αp = 0.001 with vapor−wall deposition at each initial seed surface area (Figure S7). τg,p increases by approximately half an order of magnitude for all seed surface areas considered but remains within roughly 1 order of magnitude of τg,w, for which vapor−wall deposition and vapor condensation remain competitive. Furthermore, differences in the values of τg,p between different initial seed surface areas remain similar throughout the simulation. These results indicate that although vapor condensation may become more kinetically limited as the oxidation progresses, the initial seed aerosol size distribution is a robust metric for comparing oxidation trajectories. Vapor−Wall Deposition Bias in SOA Yield. Figures 1−4 indicate that the mere increase of SOA yield as seed surface area increases does not, in itself, prove that vapor−wall deposition is occurring. Furthermore, separating the impacts of condensational kinetic limitations and vapor−wall deposition is not straightforward. Zhang et al.11 introduced the concept of a wall deposition bias Rwall,
deposition (not shown). Saturation concentrations were also varied to determine if the observed behavior of Zhang et al.11 could be qualitatively reproduced using the present model. Figures S2−S5 show that the behavior can be reproduced, supporting the simplifications employed in the model. More discussion is given in the Supporting Information. Influence of Reaction Time Scale. It has been observed experimentally that SOA yields are higher at faster oxidation rates, as the impact of vapor−wall deposition is lessened.33 In Figure 4, k[OH]A→B is increased by an order of magnitude
Y0 (10) Y the ratio of the SOA yield in the absence of wall deposition, Y0, to that obtained in an equivalent experiment with wall deposition, Y. Rwall is shown as a function of the seed surface area in Figure 5 for αp = 0.001, 0.01, and 1. For αp = 0.001
Figure 4. SOA yields after 20 h of simulation as a function of the initial seed surface area for simulations with αp = 0.001 for different values of k[OH]A→B, in the presence and absence of wall deposition.
R wall =
(with k[OH]B→C and k[OH]C→D again 5 times the previous k[OH]), and yields are shown after 20 h of simulation (ΔVOC will necessarily vary with k[OH]A→B because the simulations are run for the equivalent amount of time rather than equivalent amount of OH exposure). For k[OH]A→B = 10−4 s−1 in the absence of vapor−wall deposition, the yield is approximately 1.0 regardless of seed surface area. The lack of dependence of yield on surface area seems to contradict the earlier discussion of kinetically limited versus quasi-equilibrium condensational growth: because increasing k[OH]A→B decreases τrxn with respect to τg,p, the system should become more kinetically limited and show a stronger dependence on seed surface area. However, this effect is observed only if yields are considered at equivalent OH exposure times (see Figure S6). For k[OH]A→B = 10−4 s−1 in a 20 h simulation, species A is virtually depleted after 15 h. In the absence of vapor−wall deposition, the total concentration of condensable vapors (species B−D) is no longer changing except via condensation. Condensation will therefore be governed by quasi-equilibrium growth and is independent of seed surface area. In the presence of vapor−wall deposition, SOA yields maintain the surface area dependence for k[OH]A→B = 10−4 s−1 because vapor−wall deposition causes condensation to remain kinetically limited throughout the experiment. This analysis reveals the subtleties in comparing yields measured under different experimental conditions such as different OH levels, because the effects of both kinetic condensation limitations and vapor−wall deposition will change with both the rate of oxidation and the duration of an experiment.
Figure 5. Wall deposition bias, Rwall = Y0/Y, as a function of the initial seed surface area at different values of the vapor−particle accommodation coefficient αp with an initial VOC mixing ratio of 40 ppb and k[OH]A→B = 10−5 s−1.
(and, to a lesser extent, αp = 0.01), Rwall decreases as the seed surface area increases and then reaches a plateau, as observed experimentally in ref 11. The analysis presented here suggests that the behavior of Rwall at low surface areas is influenced by the kinetic limitations that are a consequence of a small αp. Furthermore, Rwall changes with k[OH]A→B and G0A because 10256
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AC4 program, Award No. NA13OAR4310058; and the State of California Air Resources Board, Contract 12-312.
these parameters affect yields calculated both in the presence and absence of vapor−wall deposition. The multi-faceted dependencies of SOA yield and Rwall complicate the extrapolation of chamber-derived yields to atmospheric models. If condensation in the atmosphere is dominated by quasi-equilibrium growth, chamber experiments should be carried out, if possible, at high seed surface areas, with high G0A and under rapid oxidation conditions, to minimize the effects of both kinetic limitations and vapor−wall deposition. If, however, condensation in the atmosphere is also kinetically limited, chamber experiments can be conducted at seed concentrations typical of those in the atmosphere and a vapor−particle dynamics model, similar to those presented here and in ref 11, can be used in order to correct for vapor−wall deposition. Thus, challenges will need to be met in designing experiments that simultaneously minimize the magnitude of vapor deposition to the chamber walls yet ensure conditions similar to those encountered in the ambient atmosphere. The strong sensitivity of Rwall to the value of the vapor−particle accommodation coefficient αp points to a need for constraining the value of this parameter, establishing the extent to which it varies among different chemical systems and under differing reaction conditions, and ultimately determining a value most relevant for the atmosphere. Effect of Semi-solid SOA. The present simulations do not explicitly address the microphysical nature of the particles. Recent evidence suggests that SOA often exists in a semi-solid state (e.g., refs 34, 35). In such a case, τg,p increases relative to τg,w and τrxn.28 Retarded gas−particle partitioning resulting from condensed phase diffusion limitations will drive the system toward kinetically limited SOA growth, and is essentially captured by αp values
